The paradox between the numerically competent baby and the slow learning of two- to four-year-old children / La paradoja entre el bebé numéricamente competente y el lento aprendizaje de los niños de dos a cuatro años de edad

Abstract

Since the 1980s, numerous laboratory investigations have been arguing that infants are numerically competent. This work presents a critical review of this line of research. We propose that despite the repertoire of numerical abilities attributed to infants and the seemingly natural character of the very first numbers in the numerical series, the semiotic complexity of their use and comprehension poses a cognitive challenge that children undertake, motivated, supported and often guided by others. This challenge involves a high degree of semiotic organization of the material world as well as an ability to manage early sign systems, systems which children learn how to use during their first years of life and which form the platform on which numbers are based.     

出土文献中的易卦符号再认识

目前所发现的出土文献中的易卦符号,不是数字卦,也就是说并非由数字构成。数字卦所谓的集中说,十进位数制说都不能成立。这些易卦仍然是由符号构成的,对出土的易卦符号要区别经文和实际占筮,在实际占筮中应该是由四象符号构成,而在经文中则就是阴阳卦画。出土文献中两组并列的易卦,一般看作是本卦和之卦的关系,但不符合本卦和之卦的出卦概率,而符合两次占卦的出卦概率,因而实际可能是两次占筮的结果。     

A BIOSEMIOTIC APPROACH TO THE QUESTION OF MEANING

A sign is something that refers to something else. Signs, whether of natural or cultural origin, act by provoking a receptive system, human or nonhuman, to form an interpretant (a movement or a brain activity) that somehow relates the system to this “something else.” Semiotics sees meaning as connected to the formation of interpretants. In a biosemiotic understanding living systems are basically engaged in semiotic interactions, that is, interpretative processes, and organic evolution exhibits an inherent tendency toward an increase in semiotic freedom. Mammals generally are equipped with more semiotic freedom than are their reptilian ancestor species, and fishes are more semiotically sophisticated than are invertebrates. The evolutionary trend toward the production of life forms with an increasing interpretative capacity or semiotic freedom implies that the production of meaning has become an essential survival parameter in later stages of evolution.     

Young children interpret number gestures differently than nonsymbolic sets

Researchers have long been interested in the origins of humans’ understanding of symbolic number, focusing primarily on how children learn the meanings of number words (e.g., “one”, “two”, etc.). However, recent evidence indicates that children learn the meanings of number gestures before learning number words. In the present set of experiments, we ask whether children's early knowledge of number gestures resembles their knowledge of nonsymbolic number. In four experiments, we show that preschool children (n = 139 in total; age M = 4.14 years, SD = 0.71, range = 2.75–6.20) do not view number gestures in the same the way that they view nonsymbolic representations of quantity (i.e., arrays of shapes), which opens the door for the possibility that young children view number gestures as symbolic, as adults and older children do. A video abstract of this article can be viewed at https://youtu.be/WtVziFN1yuI

Highlights

• Children were more accurate when enumerating briefly-presented number gestures than arrays of shapes, with a shallower decline in accuracy as quantities increased.
• We replicated this finding with arrays of shapes that were organized into neat, dice-like configurations (compared to the random configurations used in Experiment 1).
• The advantage in enumerating briefly-presented number gestures was evident before children had learned the cardinal principle.
• When gestures were digitally altered to pit handshape configuration against number of fingers extended, children overwhelmingly based their responses on handshape configuration.

     

TRANSFORMING THEOLOGICAL SYMBOLS

In this essay I explore the need for transforming the Christian theological symbols of the Trinity, Incarnation, and Redemption, which arose in the context of neo‐Platonic metaphysics, in light of late modern, especially Peircean, metaphysics and categories. I engage and attempt to complement the proposal by Andrew Robinson and Christopher Southgate (in this issue of Zygon) with insights from the Peircean‐inspired philosophical theology of Robert Neville. I argue that their proposal can be strengthened by acknowledging the way in which theological symbols themselves have a transformative (pragmatic) effect as they are “taken” in context and “break” on the Infinite.     

Perceiving versus inferring movements to understand dynamic events: The influence of content complexity

ObjectivesWhat type of visual presentation is best in helping learners to understand the functioning of a dynamic system and under what conditions? This study investigated the effect of content complexity on perceived cognitive load and performance resulting from studying depicted movements of team play either in an explicit manner (animation) or via arrow symbols (static diagram).DesignA 2 (treatment: diagram vs. animation) × 2 (content complexity: low vs. high) between subjects design was adopted in the experiment.MethodsForty-eight university students were randomly assigned to the four study conditions and required to perform a reconstruction test and rate their perceived cognitive load following the study phase.ResultsData analyses revealed that for low-complexity content, participants exposed to the animation treatment learned more efficiently – based on the combination of learning and cognitive load scores – than those exposed to the diagram treatment. On the other hand, for high-complexity content, participants exposed to the diagram treatment learned more efficiently than those exposed to the animation treatment.ConclusionThe findings stress the importance of considering the task complexity factor when designing and presenting instructional materials to learners.